An augmented Lagrangian algorithm for multi-objective optimization

In this paper, we propose an adaptation of the classical augmented Lagrangian method for dealing with multi-objective optimization problems. Specifically, after a brief review of the literature, we give a suitable definition of Augmented Lagrangian for equality and inequality constrained multi-objec...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 77; no. 1; pp. 29 - 56
Main Authors: Cocchi, G., Lapucci, M.
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2020
Springer Nature B.V
Subjects:
Algorithms
Convergence
Convex and Discrete Geometry
Literature reviews
Management Science
Mathematics
Mathematics and Statistics
Multiple objective analysis
Nonlinear programming
Operations Research
Operations Research/Decision Theory
Optimization
Pareto optimization
Statistics
Constrained multi-objective optimization
Pareto stationarity
Augmented Lagrangian method
Global convergence
Multi-objective steepest descent
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:In this paper, we propose an adaptation of the classical augmented Lagrangian method for dealing with multi-objective optimization problems. Specifically, after a brief review of the literature, we give a suitable definition of Augmented Lagrangian for equality and inequality constrained multi-objective problems. We exploit this object in a general computational scheme that is proved to converge, under mild assumptions, to weak Pareto points of such problems. We then provide a modified version of the algorithm which is more suited for practical implementations, proving again convergence properties under reasonable hypotheses. Finally, computational experiments show that the proposed methods not only do work in practice, but are also competitive with respect to state-of-the-art methods.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-020-00204-z